Just use Tor browser? You can turn the tor part off if you need the speed.

What you want exists, have at it

As the submission shows, Tor browser isn't enough. My hypothetical browser would never have an IndexedDB API. Why should it?

"Web applications use it for offline support, caching, session state, and other local storage needs"

This use case is completely orthogonal to what my browser is meant to do. My browser would not have a concept of local storage.

The premise of starting with a modern browser and stripping away features to get privacy is flawed - it's always vulnerable to these types of things. I'm going the opposite route: Only add features if they cannot be exploited for monitoring.